Igliashon's List of

Important Rank-2 Temperaments Supported in Small ED2s (9-ED2 ~ 15-ED2)

| 9-ED2 | 10-ED2 | 11-ED2 | 13-ED2 | 14-ED2 | 15-ED2

9-ED2

Pelogic Temperament

Generator: 4\9 or 5\9 (533.33 or 666.67 cents)
Period: Octave (1200 cents)
MOS scales:
Pentatonic 2L3s: 1 3 1 1 3
Heptatonic 2L5s: 1 1 2 1 1 1 2
JI Basis: 7-limit
Mapping (with smallest generator available): [<1 2 1 3|, <0 -1 3 -5|]
Commas Tempered Out: 135/128, 21/20

August Temperament

Generator: 1\9 or 2\9 (133.33 or 266.67 cents)
Period: 1/3-octave (400 cents)
MOS scale:
Hexatonic 3L3s: 1 2 1 2 1 2
JI Basis: 7-limit
Mapping: [<3 5 7 9|, <0 -1 0 -2|]
Commas Tempered Out: 128/125, 36/35

10-ED2

Dichotic Temperament

Generator: 3\10 or 7\10 (360 or 840 cents)
Period: Octave (1200 cents)
MOS scale:
Heptatonic 3L4s: 2 1 1 2 1 2 1
Important MODMOS: 2 1 1 2 2 1 1--adds an extra 720-cent interval, similar to maqam rast
JI Basis: 2.3.5.7.13
Mapping: [<1 1 2 4 4|, <0 2 1 -4 -1|]
Commas Tempered Out: 25/24, 65/64, 64/63

11-ED2

Machine Temperament

Generator: 2\11 or 9\11 (218.18 or 981.82 cents)
Period: Octave (1200 cents)
MOS scale:
Hexatonic 5L1s: 2 2 2 2 2 1
JI Basis: 2.7.9.11.15.17
Mapping: [<1 3 3 4 5 5|, <0 -1 1 -3 -6 -5|]
Commas Tempered Out: 64/63, 99/98, 120/119, 121/119

Oregon Temperament

Generator: 3\11 or 8\11 (327.27 or 872.73 cents)
Period: Octave (1200 cents)
MOS scale:
Heptatonic 4L3s: 2 1 2 1 2 1 2
JI Basis: 2.7.9.11.15
Mapping: [<1 2 4 4 5|, <0 3 -3 -2 -4|]
Commas Tempered Out: 55/54, 64/63, 100/99

Sentry Temperament

Generator: 4\11 or 7\11 (436.36 or 763.64 cents)
Period: Octave (1200 cents)
MOS scales:
Pentatonic 3L2s: 1 3 1 3 3
Octatonic 3L5s: 1 1 2 1 1 2 1 2
JI Basis: 2.7.9.11.15
Mapping:
Commas Tempered Out: 245/243, 99/98, 55/54

13-ED2

Glacial Temperament

Generator: 2\13 or 11\13 (184.62 or 1015.38 cents)
Period: Octave (1200 cents)
MOS scales:
Hexatonic 1L5s: 2 2 2 3 2 2
Heptatonic 6L1s: 2 2 2 1 2 2 2
JI Basis: 2.5.9.11.13
Mapping: [<1 2 3 3 4|, <0 2 1 3 -2|]
Commas Tempered Out: 45/44, 81/80, 65/64

Lovecraft Temperament

Generator: 3\13 or 10\13 (276.92 or 923.08 cents)
Period: Octave (1200 cents)
MOS scales:
Pentatonic 4L1s: 3 3 3 3 1
Enneatonic 4L5s: 2 1 2 1 2 1 2 1 1
JI Basis: 2.9.11.13.21
Mapping: [<1 2 3 3 3|, <0 5 2 3 6|]
Commas Tempered Out: 144/143, 169/168, 1344/1331

Sephiroth Temperament

Generator: 4\13 or 9\13 (369.23 or 830.77 cents)
Period: Octave (1200 cents)
MOS scales:
Heptatonic 3L4s: 3 1 1 3 1 3 1
Decatonic 3L7s: 2 1 1 1 2 1 1 2 1 1
JI Basis: 2.5.11.13.17
Mapping: [<1 2 5 4 5|, <0 1 -5 -1 -3|]
Commas Tempered Out: 65/64, 170/169, 221/220

A-Team Temperament

Generator: 5\13 or 8\13 (461.54 or 738.46 cents)
Period: Octave (1200 cents)
MOS scales:
Pentatonic 3L2s: 3 2 3 2 3
Octatonic 5L3s: 2 1 2 2 1 2 2 1
JI Basis: 2.5.9.13.21
Mapping: [<1 0 2 1 4|, <0 6 3 7 1|]
Commas: 81/80, 105/104, 2250/2197

14-ED2

Semaphore Temperament

Generator: 3\14 or 11\14 (257.14 or 942.86 cents)
Period: Octave (1200 cents)
MOS scales:
Pentatonic 4L1s: 3 3 3 3 2
Enneatonic 5L4s: 2 1 2 1 2 1 2 1 2
JI Basis: 2.3.7.11
Mapping: [<1 2 3 3|, <0 -2 -1 2|]
Commas: 49/48, 99/98

15-ED2

Blacksmith Temperament

Generator: 1\15 or 2\15 (80 or 160 cents)
Period: 1/5-octave (240 cents)
MOS scale:
Decatonic 5L5s: 2 1 2 1 2 1 2 1 2 1
JI Basis: 2.3.5.7.11
Mapping: [<5 8 12 14 17|, <0 0 -1 0 1|]
Commas: 256/243, 49/48, 56/55

Augene Temperament

Generator: 1\15 or 4\15 (80 or 320 cents)
Period: 1/3-octave (400 cents)
MOS scales:
Hexatonic 3L3s: 4 1 4 1 4 1
Enneatonic 3L6s: 3 1 1 3 1 1 3 1 1
Dodecatonic 3L9s: 2 1 1 1 2 1 1 1 2 1 1 1
JI Basis: 2.3.5.7.11
Mapping: [<3 5 7 8 10|, <0 -1 0 2 2|]
Commas: 128/125, 64/63, 56/55

Triforce Temperament

Generator: 2\15 or 3\15 (160 or 240 cents)
Period: 1/3-octave (400 cents)
MOS scales:
Hexatonic 3L3s: 3 2 3 2 3 2
Enneatonic 6L3s: 2 1 2 2 1 2 2 1 2
JI Basis: 2.3.5.7.11
Mapping: [<3 4 7 8 10|, <0 2 0 1 1|]
Commas: 128/125, 49/48, 121/120

Keemun Temperament

Generator: 4\15 or 11\15 (320 or 880 cents)
Period: Octave (1200 cents)
MOS scales:
Heptatonic 4L3s: 3 1 3 1 3 1 3
Hendecatonic 4L7s: 2 1 1 2 1 1 2 1 1 2 1
JI Basis: 2.3.5.7.11
Mapping: [<1 0 1 2 4|, <0 6 5 3 -2|]
Commas: 56/55, 49/48, 100/99

Porkypine aka 2.3.5.11 Porcupine

Generator: 2\15 or 13\15 (160 or 1040 cents)
Period: Octave (1200 cents)
MOS scales:
Heptatonic 1L6s: 3 2 2 2 2 2 2
Octatonic 7L1s: 2 1 2 2 2 2 2 2
JI Basis: 2.3.5.11
Mapping: [<1 2 3 4|, <0 -3 -5 -4|]
Commas: 55/54, 100/99